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Interesting about the hospital that tried randomization, though of course in that case the budget constraint turned out not to be a hard one.

On the "uncertainty of entitlement" issue, yes but we we should remember the people who currently don't seek care at all (especially hospital care) because they know for sure they can't afford it, and people who do seek care and then get pushed into poverty because they had to pay for it in full. In my approach some people who don't currently seek care would be persuaded to do so because of the nonzero probability of getting it free, and some people currently pushed into poverty wouldn't be. Those are plusses.